how can i make uneven distribution of lattice without changing the shape of object in the beginning
I don't know if you could have something very accurate with a lattice. Maybe you should try shapekeys or, if you have a reason to prefer a modifier, the Mesh Deform modifier or even the Surface Deform, as your object is a simple plane:


Create the object A, the one you want to deform.
Create the object B, a subdivided plane, it's the object that you'll use as the Surface Deform target.
Align its edge loops with the object A vertices.
Give your object A a Surface Deform modifier, choose object B as the target, click on the Bind button.
Select the object B, go in the Properties panel > Data > Shape Keys and create the shapekeys.
Now your object A will deform rather well.